Variational convergence for nonlinear shell models with directors and related semicontinuity and relaxation results

DOI10.1007/s002050000100zbMath0969.74040OpenAlexW2016929539MaRDI QIDQ1587320

Annie Raoult, Hervé Le Dret

Publication date: 2 October 2001

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002050000100

zbMATH Keywords

three-dimensional elasticityshell theorygeneralized quasiconvexityconsistency of Cosserat hypotheseslimit nonlinear membrane modelvariational convergence method

Mathematics Subject Classification ID

Related Items (22)

Junction of a periodic family of elastic rods with a thin plate. II. ⋮ The Reissner-Mindlin plate theory via \(\Gamma\)-convergence ⋮ Hexagonal lattices with three-point interactions ⋮ Nonlinear Korn inequalities ⋮ An Eulerian formulation of a growing constrained elastic-viscoplastic generalized membrane ⋮ A relaxation result in B V × L p for integral functionals depending on chemical composition and elastic strain ⋮ Second-order analysis for thin structures. ⋮ A Naghdi type nonlinear model for shells with little regularity ⋮ A note about weak \(\ast\) lower semicontinuity for functionals with linear growth in \(W^{1,1} \times L^1\) ⋮ Another approach to the thin-film Γ-limit of the micromagnetic free energy in the regime of small samples ⋮ Numerical Analysis of a Relaxed Variational Model of Hysteresis in Two-Phase Solids ⋮ Equi-integrability results for 3D-2D dimension reduction problems ⋮ Heterogeneous Thin Films: Combining Homogenization and Dimension Reduction with Directors ⋮ Effective energy integral functionalsfor thin films on curl-free vector fields in the Orlicz–Sobolev space setting ⋮ Some relaxation results for functionals depending on constrained strain and chemical composition ⋮ Bending-torsion moments in thin multi-structures in the context of nonlinear elasticity ⋮ AN EVOLUTIONARY ELASTOPLASTIC PLATE MODEL DERIVED VIA Γ-CONVERGENCE ⋮ A \(\Gamma\)-convergence result for optimal design problems ⋮ Dimension reduction for functionals on solenoidal vector fields ⋮ Deriving new evolution equations for microstructures via relaxation of variational incremental problems ⋮ A geometrically exact Cosserat shell-model including size effects, avoiding degeneracy in the thin shell limit. I: Formal dimensional reduction for elastic plates and existence of minimizers for positive Cosserat couple modulus ⋮ JUNCTION IN A THIN MULTIDOMAIN FOR A FOURTH ORDER PROBLEM

This page was built for publication: Variational convergence for nonlinear shell models with directors and related semicontinuity and relaxation results